A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts
arXiv:2007.05862
Abstract
We show that for a potential with summable variations on an irreducible sofic shift in one dimension, the equilibrium measures are precisely the shift-invariant Gibbs measures. The main tool in the proof is a preservation of Gibbsianness result for almost invertible factor codes on irreducible shifts of finite type, which we then extend to finite-to-one codes by applying the results about equilibrium measures.
14 pages, 1 diagram. References added to earlier work by Baladi (1991) and Haydn-Ruelle (1992), who obtained very similar results to ours, of which we became aware after posting version 1